Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14583815 | C2 | semidirect |
| 2. #26012062 | C2 | semidirect |
| 4. #26011737 | C2 | semidirect |
| 5. #26011720 | C2 | semidirect |
| 6. #26011529 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011497 | C2 | semidirect |
| 9. C2×#131×C173 | C2 | semidirect |
| 20. #19149658 | C22 | semidirect |
| 25. #19149613 | C22 | semidirect |
| 26. #19149611 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 32. C2×M16×C173 | C22 | semidirect |
| 34. C22×C8×C173 | C22 | semidirect |
| 67. C2×C8×C173 | D4 | semidirect |
| 120. C173 | #3057 | semidirect |
| 123. C2×#131 | D173 | semidirect |
| 139. C2×M16 | C2×D173 | semidirect |
| 141. C22×C8 | C2×D173 | semidirect |
| 179. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| #26012062 | 2 |
| #26012055 | 2 |
| #26011737 | 2 |
| #26011720 | 2 |
| #26011529 | 2 |
| #26011501 | 2 |
| #26011497 | 2 |
| C2×#131×C173 | 2 |
| #3057 | 173 |